Analysis and Applied Mathematics Seminar
Youngjoon Hong
SungKyunKwan University (SKKU), Seoul, South Korea
Machine learning in numerical PDEs
Abstract: As artificial intelligence makes progress, deep neural nets are being
applied to increasingly complex problem setups. In response to the
emerging difficulties of these new setups, deep learning research
explores new modeling tools to enhance the predictive power of neural
nets. Differential equations are among the new tools that are being
incorporated into deep neural net models in various ways. In particular,
neural networks and deep-learning have shown promise in speeding up
scientific simulations. For solving PDEs, the goal is often to produce
a model which can be used to quickly generate sample data for
statistical analysis; this is often applied in the inverse problem of
trying to determine a system's initial conditions, given later
observations. The result is now an exciting new research field known
as scientific machine learning, where techniques such as deep neural
networks and statistical learning are applied to classical problems
of applied mathematics. In this tutorial, our intention is to provide
an accessible introduction to recent developments in the field of
numerical solution of linear and nonlinear partial differential
equations using techniques from machine learning and artificial
intelligence.
Wednesday July 6, 2022 at 3:00 PM in 712 SEO